In his book The Mathematical Universe, mathematician William Dunham wrote of John Venn’s namesake legacy, the Venn diagram, “No one in the long history of mathematics ever became better known for less.” While Venn diagrams may not have solved any long-standing open problems, surely these interlocking rings deserve more credit. Their compact representation of group relationships explains their enduring appeal in classrooms, infographics and Internet memes.
Not merely visual aids, Venn diagrams can help us solve everyday logic problems, and they give rise to surprising geometric questions. Have you ever seen a proper Venn diagram with four overlapping circles? No, because it’s impossible. Venn himself discovered this and came up with a clever fix, but this only begot deeper geometric puzzles that mathematicians still study today.
On a blue-sky Saturday morning, I joined a foraging hike in Sintra-Cascais nature park, a former municipal wasteland and now thriving ecosystem on the outskirts of Cascais in Portugal. Progress was deliciously slow, thanks to our passionate guide – ecologist Fernanda Botelho, Portugal’s foremost herbalist and wild forager. We’d barely made it out of the park’s welcome centre when she lunged at a bush and held a spiky leaf ahoy.
“Sow thistle,” she proclaimed. “Pigs love it. It’s good for salads, but it too often gets confused with the dandelion.” Everything has its uses, she said, from pine needles for sauces and honey to ash trees for flour and berries of the Peruvian Pink Pepper tree – “planted as an ornamental tree, but it combines very well with chocolate”.
Perhaps, in the end, the measure of understanding — which is “love’s other name” — is not seeing the same light but seeing the light in each other, the shy light shimmering over the ocean of our singularity.
This edition of the Best American series is as strong as any of its predecessors, and the stories assembled here serve as excellent examples of inventive genre storytelling. The most striking of these stories invite readers to follow characters as they try to sustain relationships and a sense of self in uncertain futures—as good a theme as any for the beginning of 2025.